{
  "id": "2407.10111",
  "version": "v1",
  "published": "2024-07-14T07:47:28.000Z",
  "updated": "2024-07-14T07:47:28.000Z",
  "title": "On a characterization of probability distribution based on maxima of independent or max-independent random variables",
  "authors": [
    "B. L. S. Prakasa Rao"
  ],
  "categories": [
    "math.PR"
  ],
  "abstract": "Kotlarski (1978) proved a result on identification of the distributions of independent random variables $X,Y$ and $Z$ from the joint distribution of the bivariate random vector $(U,V)$ where $(U,V)= (\\max(X,Z),\\max(Y,Z)).$ We extend this result to the case $(U,V)=(\\max(X,aZ_1,bZ_2),\\max(Y,cZ_1,dZ_2))$ where $X,Y,Z_1,Z_2$ are independent or max-independent random variables, $Z_1$ and $Z_2$ are identically distributed and $a,b,c,d$ are known positive constants.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2024-07-14T07:47:28.000Z"
    }
  ],
  "analyses": {
    "subjects": [
      "62E10"
    ],
    "keywords": [
      "max-independent random variables",
      "probability distribution",
      "characterization",
      "bivariate random vector",
      "joint distribution"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 0,
      "language": "en",
      "license": "arXiv",
      "status": "editable"
    }
  }
}